Enter T or F depending on whether the statement is true or false. Assume that matrices in the following statements are all square and of the same size.   1. If D1 and D2 are diagonal matrices, then D2D1=D1D2.   2. If L is a lower triangular matrix and D is a diagonal matrix, then LD=DL.   3. Every upper triangular matrix can be broken into the sum of a diagonal matrix and an upper triangular matrix that has all zeros on its diagonal.   4. If U1 and U2 are upper triangular matrices, then U2U1=U1U2.   5. Every invertible upper triangular matrix can be broken into the product of a diagonal matrix and an upper triangular matrix that has all ones on its diagonal.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 21T
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Enter T or F depending on whether the statement is true or false. Assume that matrices in the following statements are all square and of the same size.

  1. If D1 and D2 are diagonal matrices, then D2D1=D1D2.
  2. If L is a lower triangular matrix and D is a diagonal matrix, then LD=DL.
  3. Every upper triangular matrix can be broken into the sum of a diagonal matrix and an upper triangular matrix that has all zeros on its diagonal.
  4. If U1 and U2 are upper triangular matrices, then U2U1=U1U2.
  5. Every invertible upper triangular matrix can be broken into the product of a diagonal matrix and an upper triangular matrix that has all ones on its diagonal.

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